/// <summary>
/// 求外部点到圆的切线
/// </summary>
/// <param name="outPoint">在圆上/圆内不计算切线</param>
/// <param name="leftTangent">逆时针切线</param>
/// <param name="rightTangent">顺时针切线</param>
/// <returns></returns>
public bool GetTangent(Double2 outPoint, ref Double2 leftTangent, ref Double2 rightTangent)
{
Double2 diff = this.circleCenter - outPoint;
double sqrDiff = diff.sqrMagnitude;
double sqrRadius = this.radius * this.radius;
// 先求切线的长度sqr
double sqrtLen = sqrDiff - sqrRadius;
if (sqrtLen <= 0)
{
return(false);
}
else
{
// 再求斜边的高度平方
double sqrHeight = sqrtLen * sqrRadius / sqrDiff;
// 求垂线。
Double2 aix = -Double2.Perpendicular(diff);
// 再求斜边的垂足。
double value = (sqrtLen - sqrHeight) / sqrDiff;
Double2 aixPos = System.Math.Sqrt((float)value) * diff + outPoint;
// 再求2个切点。
double height = System.Math.Sqrt((float)sqrHeight);
leftTangent = aixPos - aix.normalized * height - outPoint;
rightTangent = aixPos + aix.normalized * height - outPoint;
return(true);
}
}
/// <summary>
/// 创建外接圆
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="p3"></param>
/// <returns></returns>
public static Circle2D CreateCircumCircle(Double2 p1, Double2 p2, Double2 p3)
{
// 排除三点共线
Double2 diff1 = p2 - p1;
Double2 diff2 = p3 - p1;
if (diff1 == Double2.zero || diff2 == Double2.zero)
{
return(null);
}
double value = Double2.Cross(diff1, diff2);
if (System.Math.Abs(value) < MathUtil.kEpsilon)
{
return(null);
}
// 2垂直平分线就是圆心。
Double2 mid1 = p1 + diff1 * 0.5f;
Double2 mid2 = p1 + diff2 * 0.5f;
Line2D line1 = new Line2D(mid1, Double2.Perpendicular(diff1));
Line2D line2 = new Line2D(mid2, Double2.Perpendicular(diff2));
Double2 center = Double2.zero;
if (line1.GetIntersectPoint(line2, ref center) == true)
{
double radius = (center - p1).magnitude;
return(new Circle2D(center, radius));
}
else
{
return(null);
}
}
/// <summary>
/// DrawGizmos
/// </summary>
public void DrawGizmos()
{
startPoint.DrawGizmos();
Double2 v1 = Double2.Perpendicular(normalizedDir).normalized * 0.2f;
Double2 diff = 9.8f * normalizedDir;
UnityEngine.Gizmos.DrawLine((startPoint + diff + v1).V3, EndPoint);
UnityEngine.Gizmos.DrawLine((startPoint + diff - v1).V3, EndPoint);
}
/// <summary>
/// 初始化数据
/// </summary>
/// <param name="points"></param>
private void Init(Double2[] points)
{
if (points == null || points.Length < 3)
{
return;
}
this.pointArr = new Double2[points.Length];
this.normalAttr = new Double2[points.Length];
this.distancArr = new double[points.Length + 1];
Double2 min = points[0];
Double2 max = points[0];
int i;
for (i = 0; i < points.Length; i++)
{
this.pointArr[i] = points[i];
if (i > 0)
{
min = Double2.Min(min, points[i]);
max = Double2.Max(max, points[i]);
totalDistance += MathUtil.GetNearDistance(points[i - 1], points[i]);
this.distancArr[i] = totalDistance;
}
else
{
min = points[i];
max = points[i];
this.distancArr[i] = 0;
totalDistance = 0;
}
//
Double2 dir;
if (i < points.Length - 1)
{
dir = (points[i + 1] - points[i]).normalized;
}
else
{
dir = (points[0] - points[i]).normalized;
}
this.normalAttr[i] = Double2.Perpendicular(dir);
}
totalDistance += MathUtil.GetNearDistance(points[points.Length - 1], points[0]);
this.distancArr[i] = totalDistance;
this.SetAABB(min, max);
}